If the current in an AC circuit is given as $\mathrm{i}=\left(5\mathrm{A}\right)\sin \left(\mathrm{\omega t}-\frac{\mathrm{\pi }}{3}\right)$ when an emf $\mathrm{e}=\left(200\mathrm{V}\right)\mathrm{sin\omega t}$ is applied across the circuit. The circuit has components-

1.  L and C

2.  L and R

3.  C and R

4.  None of these

A step-down transformer is employed to reduce the main supply of AC from 220V to 11V. If the primary coil draws a current of 5A and the secondary supplies a current of 90A, then the efficiency of the transformer is  -

1.  10%

2.  95%

3.  90%

4.  80%

At resonance, the value of the power factor of the circuit is -

1.  1

2.  Zero

3.  Between zero and 1

4.  More than 1

In a LCR circuit having L = 8.0 henry, C = 0.5 $\mathrm{\mu F}$ and R = 100 $\mathrm{\Omega }$ in series, the resonance frequency (in Hz) is 

1.  $\frac{250}{\mathrm{\pi }}\mathrm{Hz}$

2.  $\frac{600}{\mathrm{\pi }}\mathrm{Hz}$

3.  $\frac{500}{\mathrm{\pi }}\mathrm{Hz}$

4.  $500 \mathrm{Hz}$

In an \(LCR\) series network, \(V_L = 40~\text{V}, V_C = 20~\text{V}~\text{and}~V_R = 15~\text{V}.\) The supply voltage will be:
1. \(25~\text{V}\)
2. \(75~\text{V}\)
3. \(35~\text{V}\)
4. zero

The ratio of the number of turns in secondary to primary in an ideal transformer varies from 50 to 550. If the power input is P, then its output power is  -

1.  11P

2.  $\frac{\mathrm{P}}{11}$

3.  $\frac{18P}{111}$

4.  P

Loss in energy in the transformer is due to 

1.  Hysteresis

2.  Eddy current loss

3.  Leakage of flux

4.  All of these